Accurate prediction of band gaps and optical properties of HfO2

Abstract

We report on optical properties of various polymorphs of hafnia predicted within the framework of density functional theory. The full potential linearised augmented plane wave method was employed together with the Tran–Blaha modified Becke–Johnson potential (TB-mBJ) for exchange and local density approximation for correlation. Unit cells of monoclinic, cubic and tetragonal crystalline, and a simulated annealing-based model of amorphous hafnia were fully relaxed with respect to internal positions and lattice parameters. Electronic structures and band gaps for monoclinic, cubic, tetragonal and amorphous hafnia were calculated using three different TB-mBJ parametrisations and the results were critically compared with the available experimental and theoretical reports. Conceptual differences between a straightforward comparison of experimental measurements to a calculated band gap on the one hand and to a whole electronic structure (density of electronic states) on the other hand, were pointed out, suggesting the latter should be used whenever possible. Finally, dielectric functions were calculated at two levels, using the random phase approximation without local field effects and with a more accurate Bethe–Salpether equation (BSE) to account for excitonic effects. We conclude that a satisfactory agreement with experimental data for HfO2 was obtained only in the latter case.